Evnetually they'll be nothing left to catch. The fishstocks of the world's oceans are already dangerously low. Aside from whales and dolphins, the Japanese do not appear to be self-policing and/or self-limiting in what they catch. I've seen red-snappers and other fish in the supermarkets that were babies, barely any meat on them and they probably never had a chance to reproduce. Any culture has to weigh its traditions against, at the very least, its own survival. If its an intelligent and benvolent culture, it also has to weigh its traditions against the survivial of the rest of the world. This latter situation is only becoming an issue in this day and age, where countries can actually have a global impact.
We in the west, if you can call it a tradition, love our energy guzzling cars and appliances - we need to change that. Japan and Denmark need to re-evaluate the long term pros and cons of continuing their fishing practices both for the purpose of food and also preventing the extinction of a species we still have much to learn from.